Abstract:Discrete tomography differs from standard computerized tomography since it deals with the reconstruction of objects made of just one homogeneous material. In this case, we assume their shapes through a priori knowledge and reduce the number of projections to no more than four. Several issues arise due to this dearth of input data. For example, the consistency problem coincides with the ability to state whether there exists any object compatible with a given set of projections; the uniqueness problem derives from the fact that different objects can lead to the same projections; the stability problem concerns how the shape of an object changes while perturbing its projections. Possible applications include non-destructive reverse engineering, industrial quality control, electron microscopy, X-rays crystallography, data coding and compression.<br>
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We developed genetic and memetic algorithms to reconstruct both convex planar sets (which are usually studied in literature) and binary images of whatever shape, giving a quantitative estimate for both the probability of finding solutions and of introducing errors at a given rate of noise in the projections (in order to simulate an instrumental error). We verified the results obtained through our new methods on real images coming from biomedical tests, too. Extensive experiments have been carried out to compare our new methodologies with a generalized version of a well known algorithm, originally proposed by Del Lungo and Kuba. Preliminary results suggest that our methods are robust, even for images without a priori model. On this subject, we intend to generalize the algorithm to take into account also specific information about the images to study. For instance, we plan to extend the method to three-dimensional volumes of data, considering also that successive slices are usually similar one to each other.
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Usually, evolutionary approaches benefit from parallel implementations on both High Performance Computers and Grid Architectures. In fact, it is quite